From your text, we can say that , where R represents the event "egg rotten" and A the even "egg provided by A".
We also have
What we are looking for is , that is to say "if the egg is rotten (condition), what is the probability that it was supplied by A (event)"
Now, let X be the number of eggs supplied by B.
A will supply 3X eggs.
The total is 4X.
So the probability to take an egg from A is
With the formula of conditional probability, we have